Solve Inequality in Terms of Other Variables
Read this topicProblems 38
- If bbb is a positive constant, solve bx>5bbx > 5bbx>5b for xxx.
- Which of the following compound inequalities is equivalent to −2x<−5q<−8-2x < -5q < -8−2x<−5q<−8?
- Which of the following points are solutions to the inequality x−3<y≤x+3x-3 < y \leq x + 3x−3<y≤x+3?
- Solve for xxx. 4x−3y+5(x+y)≥4(x−y)+2(x+x)+7y4x-3y+5(x+y)\geq4(x-y)+2(x+x)+7y4x−3y+5(x+y)≥4(x−y)+2(x+x)+7y
- If x,l,α,ε>0x, l, \alpha, \varepsilon>0x,l,α,ε>0, solve for yyy in terms of x,l,α,εx, l, \alpha, \varepsilonx,l,α,ε. y2xl<αε2\frac{y}{2xl}<\frac{\alpha\varepsilon}{2}2xly<2αε
- Which inequalities below are equivalent to 3x+9<6y3x+9<6y3x+9<6y?
- Which value of α\alphaα makes the inequality αx−α<6\alpha x - \alpha < 6αx−α<6 equivalent to the inequality x<7x<7x<7?
- Are these inequalities equivalent? 4x+y−3z<18z>4x3+y3+6\begin{gather} 4x+y-3z<18\\ z>\frac{4x}{3}+\frac{y}{3}+6 \end{gather}4x+y−3z<18z>34x+3y+6
- Which inequalities are equivalent? Ineq 1: 2(x−1)<y+4Ineq 2: y>2(x−3)Ineq 3: −x<−(y2+3)\begin{align} &\text{Ineq 1: }\ 2(x-1)<y+4\\ &\text{Ineq 2: }\ y>2(x-3)\\ &\text{Ineq 3: }…
- Let β\betaβ be a real constant. What value of α\alphaα makes the following inequalities equivalent? 2x−α<3y+βx<32(y+β)\begin{gather} 2x-\alpha<3y+\beta\\ x<\frac{3}{2}(y+\beta) …
- Solve for xxx in terms of yyy. 3(x−1)−2<−2(y−(−1))3(x-1)-2<-2(y-(-1))3(x−1)−2<−2(y−(−1))
- Solve for xxx in terms of yyy. 3(x−2y+2)+7<−(x+2y)+83(x-2y+2)+7<-(x+2y)+83(x−2y+2)+7<−(x+2y)+8
- Solve for xxx in terms of yyy and α\alphaα, if α>0\alpha>0α>0. x+3α−2y<3α−y\frac{x+3}{\alpha}-2y<\frac{3}{\alpha}-yαx+3−2y<α3−y
- Solve for xxx if y>0y>0y>0. 3y(1−xy)>2(x+6y−14)3y(1-\frac{x}{y})>2(x+6y-14)3y(1−yx)>2(x+6y−14)
- Solve for xxx if α\alphaα, β\betaβ, δ\deltaδ, ϵ\epsilonϵ, λ>0\lambda>0λ>0. α(x+β)+δ>ϵy+λ\alpha(x+\beta)+\delta>\epsilon y+\lambdaα(x+β)+δ>ϵy+λ
- Solve for xxx in terms of yyy. 4(x+8)>9y+3(2x−1)4(x+8)>9y+3(2x-1)4(x+8)>9y+3(2x−1)
- Solve for xxx in terms of yyy. 3(2x−y+6)−13<19(y+2x−4)3(2x-y+6)-13<19(y+2x-4)3(2x−y+6)−13<19(y+2x−4)
- Describe the solutions of the following inequality. 4(3x+y−z+2)<2(2x−2z+1)+4(2x+y+3)4(3x+y-z+2)<2(2x-2z+1)+4(2x+y+3)4(3x+y−z+2)<2(2x−2z+1)+4(2x+y+3)
- For what values of α\alphaα is the following inequality true whenever xxx is real and y>0y > 0y>0 is a positive real number? 6(x+2y+4)≥3(2x+αy+8)6(x+2y+4)\geq3(2x+\alpha y+8)6(x…
- At the very least, how much bigger must yyy be than xxx in order to satisfy the inequality y≥x+3y \ge x + 3y≥x+3?
- Which of the following points (as graphed above) satisfy the inequality y>x+3y > x + 3y>x+3?
- Which of the following compound inequalities is equivalent to 2x−3<x+y≤2x+32x-3 < x + y \leq 2x + 32x−3<x+y≤2x+3?
- Which of the following compound inequalities is equivalent to 5x−2<2x+y≤3x+1?5x-2 < 2x + y \leq 3x + 1?5x−2<2x+y≤3x+1?
- Which of the following compound inequalities is equivalent to 2+6x<y+x−1≤x+4?2+6x < y + x - 1 \leq x+4?2+6x<y+x−1≤x+4?
- Which of the following compound inequalities is equivalent to 3x+2<y−3≤x−1?3x+2< y - 3 \leq x-1?3x+2<y−3≤x−1?
- Solve the inequality for yyy: 4x+6<2y−24x+6<2y-24x+6<2y−2
- Solve the inequality for yyy: 5x+3<3y−x5x+3<3y-x5x+3<3y−x
- Solve the inequality for yyy: 7x+9≤2y−x+17x+9\leq 2y-x+17x+9≤2y−x+1
- Solve the inequality for yyy: 4x−10≤−5y−x4x-10\leq -5y-x4x−10≤−5y−x
- Solve the inequality for yyy: 9x+2≥−4y+x−29x+2\geq -4y+x-29x+2≥−4y+x−2
- Which point satisfies the inequality y<4x−2?y<4x-2?y<4x−2?
- Which point satisfies the inequality 2y<4x−2?2y<4x-2?2y<4x−2?
- Which point satisfies the compound inequality x+2≤y≤2x+1?x+2\leq y\leq 2x+1?x+2≤y≤2x+1?
- Find an equivalent inequality to y>3x+9y > 3x+9y>3x+9 by dividing both sides by 3 and then subtracting 3 from both sides.
- Find an equivalent inequality to 5y>10x+205y > 10x+205y>10x+20 by dividing both sides by 5, subtracting 4 from both sides, and then dividing both sides by 2.
- If ccc is a negative constant, solve xc>5xc>5xc>5 for xxx.
- If ccc is a negative constant, solve for xxx in the inequality cx+3>5cx+3>5cx+3>5.
- Select the inequalities that can also be expressed as: 4x−8y≥124x-8y \geq 124x−8y≥12